I have a squealy floor below my carpet on the 2nd floor of my house. It sounds like the subfloor under the carpet is moving up and down a little and makes this awful load squeak when I step down on this specific location. It can be reproduced at will.
Fixing a squeaky floor beneath a carpet is a fairly complicated process that's probably best illustrated with video. This Old House provides a wonderful tutorial.
The procedure demonstrated at that link does not require you to pull up any carpet and uses scored screws to hide your work. This seems to be the most hassle-free way to do what one might expect to be a huge job.
If there's movement you'd do best to pull back the carpet and nail down the subfloor. Hopefully the squeak isn't in the middle of the room.
I had a squeaky floor at an old house, had to pull back a large chunk of carpet and drive a few nails through the floor to anchor it down.
Best of luck.